I think Presonus Studio One is free as well, also a viable option. I'd go with Reaper because it behaves more like a normal DAW and has all your bells and whistles. Plenty others out there though that will offer free trials. If you have the money for it, I recommend Cubase, purely because that's what I've used all my recording life. I wrote a little blog post on this very thing not long ago: ĮDIT: I only recommended Audacity as a completely free 'way in' to DAWs, to learn the very basics. If there's anything you don't understand then feel free to hit me up. I'm happy to answer any questions here, I'm a DIY-producer and this is how I spend most of my spare time, specifically on a low budget.
GarageBand is an incredible tool for songwriters just starting out, if you have a mac, as it has a lot of this built in.
the software you are using to record audio, such as Audacity), they won't sound like the real thing on a budget but are great fun to work with if you don't have access to those instruments. software that runs inside the recording app), if you want to add drums or piano, for instance, available for most DAWs (Digital Audio Workstation - i.e. There's lots of options for virtual instruments (i.e. But you don't need to break the bank, no matter what some experts may claim. This will sound HORRIBLE but means you can get to grips with the basics without spending a dime, and if you're happy you want to progress it is worth putting a little money towards it.
I don't know what your computer situation is, but as a test you can download Audacity and use the internal microphone on the laptop if you're on a super-tight budget. I recommend a Shure SM57 for both instrument and vocal recording, but again there's a lot of options. You will anyway if you want to record vocals too. Obviously this means you'll need to get a microphone. This means pointing a microphone at your amp and connecting the mic to the audio interface. Then you have a couple of options - you can either plug your guitar into the audio interface (which is connected to your computer, running Audacity) either directly in or via the 'phones' output on the 50xl, or you can mic up your guitar amp. I recommend between £80-100 (little more in dollars) to get something decent and future proof if you want more than 1 input at a time. These are PLENTIFUL and come in all shapes and sizes, and will connect usually via USB/thunderbolt, but you can go real cheap for a single input device. Then all you need to get started is an audio interface. It doesn't have all the bells and whistles but will get you started and give you basic understanding of multitrack recording.
If you have a halfway-decent laptop or PC (anything really), you can get audacity for free: I created an account specifically to answer this one!